Chapter 5/Applying Consumer Theory

CHAPTER 5 Applying Consumer Theory

MULTIPLE CHOICE
Choose the one alternative that best completes the statement or answers the question.

Figure 5.1

1) Figure 5.1 shows Bobby's indifference map for juice and snacks. Also shown are three budget
lines resulting from different prices for snacks assuming he has $20 to spend on these goods.
Which of the following points are on Bobby's price-consumption curve?
A) 10 snacks and 20 juices
B) 10 snacks and 0 juices
C) 10 snacks and 5 juices
D) 10 snacks and 15 juices

Answer: D
Diff: 0
Topic: Deriving Demand Curves

2) Figure 5.1 shows Bobby's indifference map for juice and snacks. Also shown are three budget
lines resulting from different prices for snacks assuming he has $20 to spend on these goods.
Which of the following points are on Bobby's demand curve for snacks?
A) p = 2, q = 10
B) p = 2, q = 13
C) p = 2, q = 5
D) p = 1, q = 20

Answer: C
Diff: 1
Topic: Deriving Demand Curves

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3) Figure 5.1 shows Bobby's indifference map for juice and snacks. Also shown are three budget
lines resulting from different prices for snacks. This information could be used to determine
A) the slope of Bobby's demand curve for juice.
B) the amount by which Bobby's demand curve for juice shifts when his income rises.
C) the amount by which Bobby's demand curve for juice shifts when the price of snacks
rises.
D) All of the above.

Answer: C
Diff: 1
Topic: Deriving Demand Curves

4) Figure 5.1 shows Bobby's indifference map for juice and snacks. Also shown are three budget
lines resulting from different prices for snacks. As the price of snacks rises, Bobby's utility
A) stays the same.
B) increases.
C) decreases.
D) might change, but there is not enough information to determine.

Answer: C
Diff: 0
Topic: Deriving Demand Curves

5) Figure 5.1 shows Bobby's indifference map for juice and snacks. Also shown are three budget
lines resulting from different prices for snacks. Bobby's demand for snacks is
A) unit elastic.
B) elastic.
C) inelastic.
D) perfectly elastic.

Answer: C
Diff: 2
Topic: Deriving Demand Curves

6) As the price of a good rises, the consumer will experience

A) a desire to consume a different bundle.
B) a decrease in utility.
C) a southwesterly movement on the indifference map.
D) All of the above.

Answer: D
Diff: 1
Topic: Deriving Demand Curves
7) An increase in the price of a good causes
A) a change in the slope of the budget line.

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B) an increase in the consumption of that good.

C) a rightward shift of the demand curve for that good.
D) a parallel rightward shift of the budget line.

Answer: A
Diff: 1
Topic: Deriving Demand Curves

8) Suppose a graph is drawn to show a consumer's preferences for football tickets and
basketball tickets. The quantity of football tickets is measured on the horizontal axis. If the
price-consumption curve is horizontal when the price of football tickets changes, then
A) football tickets are an inferior good.
B) the demand for football tickets is perfectly elastic.
C) the demand for football tickets is unit elastic.
D) the demand curve for football tickets will be horizontal.

Answer: C
Diff: 2
Topic: Deriving Demand Curves

9) Suppose the quantity of x is measured on the horizontal axis. If the price consumption curve
is vertical when the price of x changes, then the demand for x is
A) perfectly elastic.
B) perfectly inelastic.
C) unit elastic.
D) There is not enough information to determine the price elasticity of demand for x.

Answer: B
Diff: 2
Topic: Deriving Demand Curves

Figure 5.2

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10) Figure 5.2 shows Larry's indifference map and budget lines for ham and pork. Which of the
following statements is TRUE?
A) Pork is an inferior good.
B) Ham is an inferior good.
C) Neither pork nor ham is an inferior good.
D) Both ham and pork are inferior goods.

Answer: B
Diff: 1
Topic: How Income Changes Shift Demand Curves

11) Figure 5.2 shows Larry's indifference map and budget lines for ham and pork. Which of the
following statements is TRUE?
A) Larry's Engel curve for pork will be upward sloping.
B) Larry's Engel curve for pork will be downward sloping.
C) Larry's Engel curve for pork will be backward bending.
D) Larry's Engel curve for pork cannot be derived from the information provided.

Answer: A
Diff: 1
Topic: How Income Changes Shift Demand Curves

12) Figure 5.2 shows Larry's indifference map and budget lines for ham and pork. Which of the
following statements is TRUE?
A) Larry's demand curve for pork shifts rightward when his income increases.
B) Larry's income elasticity of demand for pork is greater than zero.
C) Pork is a normal good.
D) All of the above.

Answer: D
Diff: 2
Topic: How Income Changes Shift Demand Curves

13) After Joyce and Larry purchased their first house, they made additional home improvements
in response to increases in income. After a while, their income rose so much that they could
afford a larger home. Once they realized they would be moving, they reduced the amount of
home improvements. Their Engel curve for home improvements on their current home is
A) negatively sloped.
B) flat.
C) positively sloped.
D) backward bending.

Answer: D
Diff: 2
Topic: How Income Changes Shift Demand Curves

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14) Suppose the quantity of x is measured on the horizontal axis. If the income consumption
curve is vertical, then the income elasticity of demand for x is
A) 0.
B) 1.
C) -1.
D) There is not enough information to determine the income elasticity of demand for x.

Answer: A
Diff: 2
Topic: How Income Changes Shift Demand Curves

Figure 5.3

15) When John's income was low, he could not afford to dine out and would respond to a pay
raise by purchasing more frozen dinners. Now that his income is high, a pay raise causes him
to dine out more often and buy fewer frozen dinners. Which graph in Figure 5.3 best
represents John's Engel curve for frozen dinners?
A) Graph A
B) Graph B
C) Graph C
D) Graph D

Answer: A
Diff: 2
Topic: How Income Changes Shift Demand Curves

16) When John's income was low, he could not afford to dine out and would respond to a pay
raise by purchasing more frozen dinners. Now that his income is high, a pay raise causes him
to dine out more often and buy fewer frozen dinners. Which graph in Figure 5.3 best
represents John's Engel curve for dining out?
A) Graph A

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B) Graph B
C) Graph C
D) Graph D

Answer: B
Diff: 2
Topic: How Income Changes Shift Demand Curves

17) Even though Mary's income is very low, she makes sure that she purchases enough milk for
her family to drink. As her income rises, she does buy more milk. Which graph in Figure 5.3
best represents Mary's Engel curve for milk?
A) Graph A
B) Graph B
C) Graph C
D) Graph D

Answer: C
Diff: 2
Topic: How Income Changes Shift Demand Curves

18) When John was in college and his income was low, he drank "Red Ribbon" beer. As his
income increased, he purchased better-quality beer and less "Red Ribbon." Which graph in
Figure 5.3 best represents John's Engel curve for "Red Ribbon" beer?
A) Graph A
B) Graph B
C) Graph C
D) Graph D

Answer: D
Diff: 2
Topic: How Income Changes Shift Demand Curves

19) Which graph in Figure 5.3 best represents a good that is an inferior good at some
income levels, and a normal good at other income levels?
A) Graph A
B) Graph B
C) Graph C
D) Graph D

Answer: A
Diff:1
Topic: How Income Changes Shift Demand Curves

20) Median household income is $50,000 per year. The typical household spends about $125 per
year on milk, which has an income elasticity of about 0.07. From this information, we can
conclude that

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A) milk is a luxury.
B) milk is a Giffen good.
C) the income effect from a change in the price of milk is very large.
D) the income effect from a change in the price of milk is very small.

Answer: D
Diff: 2
Topic: Effects of a Price Change
21) When the price of a good changes, the total effect of the price change on the quantities
purchased can be found by comparing the quantities purchased
A) on the old budget line and the new budget line.
B) on the original indifference curve when faced with the original prices and when faced with
the new prices.
C) on the new budget line and a hypothetical budget line that is a parallel shift back to the
original indifference curve.
D) on the new indifference curve.

Answer: A
Diff: 2
Topic: Effects of a Price Change

22) When the price of a good changes, the substitution effect can be found by comparing the
equilibrium quantities purchased
A) on the old budget line and the new budget line.
B) on the original indifference curve when faced with the original prices and when faced with
the new prices.
C) on the new budget line and a hypothetical budget line that is a parallel shift back to the
original indifference curve.
D) on the new indifference curve.

Answer: B
Diff: 2
Topic: Effects of A Price Change

23) Suppose that frozen dinners were once a normal good for John, but now frozen dinners are an
inferior good for him. John's demand curve for frozen dinners
A) has become steeper as a result.
B) has become flatter as a result.
C) has not changed as a result.
D) has disappeared as a result.

Answer: A
Diff: 2
Topic: Effects of a Price Change

24) One characteristic of a Giffen good is that it

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A) is a luxury good.
B) is an inferior good.
C) has an upward-sloping Engel curve.
D) All of the above.

Answer: B
Diff: 2
Topic: Effects of a Price Change
25) If a good is an inferior good, then its
A) demand curve will be upward sloping.
B) income effect reinforces the substitution effect.
C) income elasticity is negative.
D) Engel curve cannot be drawn.

Answer: C
Diff: 2
Topic: Effects of a Price Change

26) Suppose Lisa spends all of her money on books and coffee. When the price of
coffee decreases, the
A) substitution effect on coffee is positive, and the income effect on coffee is positive.
B) substitution effect on coffee is ambiguous, and the income effect on coffee is ambiguous.
C) substitution effect on coffee is positive, and the income effect on coffee is ambiguous.
D) substitution effect on coffee is ambiguous, and the income effect on coffee is positive.

Answer: C
Diff: 1
Topic: Effects of a Price Change

27) In the case of a normal good

A) demand curves always slope downward.
B) the income effect and substitution effect are in the same direction.
C) the Engel curve slopes upward.
D) All of the above.

Answer: D
Diff: 2
Topic: Effects of A Price Change

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Figure 5.4

28) Figure 5.4 shows Bobby's indifference map for soda and juice. B1 indicates his original
budget line. B2 indicates his budget line resulting from a decrease in the price of soda. What
change in quantity best represents his substitution effect?
A) 3
B) 10
C) 15
D) 7

Answer: A
Diff: 2
Topic: Effects of a Price Change

29) Figure 5.4 shows Bobby's indifference map for soda and juice. B1 indicates his original
budget line. B2 indicates his budget line resulting from a decrease in the price of soda. What
change in quantity best represents his income effect?
A) 3
B) 10
C) 15
D) 7

Answer: D
Diff: 2
Topic: Effects of a Price Change

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30) Figure 5.4 shows Bobby's indifference map for soda and juice. B1 indicates his original
budget line. B2 indicates his budget line resulting from an increase in the price of soda. From
the graph, one can conclude that
A) Bobby views soda as an inferior good.
B) Bobby's demand for soda is perfectly inelastic.
C) Bobby views soda as a normal good.
D) the income elasticity of demand for soda is 1.

Answer: C
Diff: 2
Topic: Effects of a Price Change

31) The Slutsky equation shows that, holding the total effect constant, the income effect will be
larger for goods that
A) have a smaller substitution effect.
B) make up a larger percentage of a household's budget.
C) have perfectly inelastic demand curves.
D) All of the above.

Answer: B
Diff: 2
Topic: Effects of a Price Change

32) Suppose that the interest rate paid to savers increases. As a result, Tom wishes to save less.
This suggests that, for Tom,
A) the substitution effect is greater than the income effect.
B) the income effect is greater than the substitution effect.
C) utility maximization is not occurring.
D) future consumption is a luxury.

Answer: B
Diff: 2
Topic: Effects of a Price Change

33) Suppose that the interest rate paid to savers increases. As a result, Tom wishes to save more.
This suggests that, for Tom,
A) the substitution effect is greater than the income effect.
B) the income effect is greater than the substitution effect.
C) utility maximization is not occurring.
D) future consumption is a luxury.

Answer: A
Diff: 2
Topic: Effects of a Price Change

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34) A consumer price index adjustment overcompensates for inflation because it ignores
34 A) the income effect when relative prices change.
B) the substitution effect when relative prices change.
C) that some goods are inferior.
D) that the substitution effect may offset the income effect.

Answer: B
Diff:0
Topic: Cost-of-Living Adjustments

35) Employing a fixed-weight index like the Consumer Price Index to adjust a person's salary in
response to inflation will overcompensate this person because doing so will allow this person
to
A) buy the same bundle of goods as he did before the inflation.
B) achieve a higher level of utility than he did before the inflation.
C) achieve the same level of utility as before the inflation.
D) buy more of all goods.

Answer: B
Diff: 2
Topic: Cost-of-Living Adjustments

36) Under which of the following conditions will there be no substitution bias in the CPI?
A) Indifference curves are convex.
B) Indifference curves are L shaped.
C) Indifference curves are linear.
D) Indifference curves are downward sloping.

Answer: B
Diff: 2
Topic: Cost-of-Living Adjustments

37) Under which of the following conditions will there be no substitution bias in the CPI?
A) Lower-priced goods increase in price by a greater percentage than do higher-priced goods.
B) Higher-price goods increase in price by a greater percentage than do lower-priced goods.
C) All goods change in price by the same amount.
D) All goods change in price by the same percentage.

Answer: D
Diff: 2
Topic: Cost-of-Living Adjustments

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38) A true cost-of-living adjustment in response to a change in prices would compensate

consumers so that they will be able to
A) purchase the same bundle they purchased before prices changed.
B) achieve the same level of utility they did before prices changed.
C) face the same choices they did before prices changed.
D) achieve an increase in utility that is equal to the rate of inflation.

Answer: B
Diff: 2
Topic: Cost-of-Living Adjustments

39) If a person supplies more hours of labor in response to a wage increase, then
A) the substitution effect is greater than the income effect.
B) the income effect is greater than the substitution effect.
C) the income effect equals the substitution effect.
D) the person is not maximizing utility.

Answer: A
Diff: 1
Topic: Deriving Labor Supply Curves

40) If a person supplies less hours of labor in response to a wage increase, then
A) the substitution effect is greater than the income effect.
B) the income effect is greater than the substitution effect.
C) the income effect equals the substitution effect.
D) the person is not maximizing utility.

Answer: B
Diff: 1
Topic: Deriving Labor Supply Curves

41) A backward-bending labor supply curve implies that

A) the substitution effect dominates the income effect at higher wage rates but not at lower
wage rates.
B) the substitution effect dominates the income effect at lower wage rates but not at higher
wage rates.
C) leisure is an inferior good.
D) workers are irrational.

Answer: B
Diff: 1
Topic: Deriving Labor Supply Curves

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42) If Bobby thinks that leisure is an inferior good, then his labor supply curve
A) is backward bending.
B) is always negatively sloped.
C) is always positively sloped.
D) does not exist.

Answer: C
Diff: 1
Topic: Deriving Labor Supply Curves

43) A tax cut that raises the after-tax wage rate will most likely result in more hours worked if
A) tax rates were low already.
B) the relevant portion of the labor supply curve is upward sloping.
C) the relevant portion of the labor supply curve is downward sloping.
D) workers can be easily fooled.

Answer: B
Diff: 1
Topic: Deriving Labor Supply Curves

44) If workers are in the backward-bending section of their labor supply curves, than
an increase in the income tax rate will
A) increase the tax revenue and increase the number of hours worked.
B) increase the tax revenue and decrease the number of hours worked.
C) decrease the tax revenue and increase the number of hours worked.
D) decrease the tax revenue and decrease the number of hours worked.

Answer: A
Diff: 2
Topic: Deriving Labor Supply Curves

45) In response to an increase in the wage rate, the substitution effect will cause a person to
A) supply fewer hours of labor.
B) supply more hours of labor.
C) supply the same hours of labor.
D) have a backward bend in her labor supply curve.

Answer: B
Diff: 1
Topic: Deriving Labor Supply Curves

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46) In response to an increase in the wage rate, the income effect will cause a person to
A) supply fewer hours of labor.
B) supply more hours of labor.
C) supply the same hours of labor.
D) have a horizontal labor supply curve.

Answer: A
Diff: 1
Topic: Deriving Labor Supply Curves

TRUE/FALSE/EXPLAIN

1) If the price-consumption curve is upward sloping when the price of the good measured on the
horizontal axis changes, then the demand curve for that good will be upward sloping.

Answer: False. An upward-sloping price-consumption curve indicates that as the price of the
good falls, more of both goods will be purchased. So, the demand curve for the good
measured on the horizontal axis slopes downward.
Diff: 1
Topic: Deriving Demand Curves

2) If a consumer is compensated for the income effect that occurs when the price of a good
increases, then his demand curves can never slope upward.

Answer: True. The demand curve would only include the substitution effect. Even for Giffen
goods, dq/dp is negative holding utility constant.
Diff: 1
Topic: Effects of A Price Change

3) If the Engel curve for a good is upward sloping, the demand curve for that good must be
downward sloping.

Answer: True. If the Engel curve is upward sloping, the good is normal. As a result, the
income effect will reinforce the substitution effect and guarantee a downward-sloping
demand curve.
Diff: 1
Topic: Effects of a Price Change

4) Using the CPI to compensate workers for inflation is appropriate because, in the face of a
change in relative prices, people should be allowed to purchase the same bundle as they did
before the price changes.

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Answer: False. This assumes that people would still prefer the original bundle. Because they
are facing a new set of relative prices, compensating people so that they could purchase the
original bundle will allow them to be able to achieve a higher level of utility than they did
before the price changes.
Diff: 1
Topic: Cost-of-Living Adjustments

5) A tax cut will unambiguously lower income-tax revenue.

Answer: False. It depends on how the quantity of labor supplied responds to the increase in
the after-tax wage rate. If the income effect dominates, the quantity of labor supplied falls
and so will tax revenue. If the substitution effect dominates, the quantity of labor supplied
increases, and income-tax revenue could increase. This is a function of whether the after tax
wage was low already because the tax rate was relatively high.
Diff: 1
Topic: Deriving Labor Supply Curves

PROBLEMS

Figure 5.5

1) Suppose Joe earns $1,000 in year 1 and $0 in year 2. Any amount he saves will earn interest
at a rate of 10%. Draw Joe's budget line. (Hint: He can either consume all $1000 this year or
consume nothing this year and have $1,100 next year.) Assuming convex indifference curves,
show that an increase in the rate of interest can cause Joe's savings to either increase or
decrease. Explain in terms of income and substitution effect.

Answer: See Figure 5.5. On the graph, his original bundle is e1 so that his savings equal 1000
- C1*. A higher interest rate rotates the budget line so that, depending on the shape of his
indifference map, he may choose either e2, which means savings increase, or e3, which means
savings decrease. One plus the interest rate represents the price of current consumption. A

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higher interest rate has two effects. The substitution effect means that Joe will save more
because current consumption has become more expensive. The income effect says Joe will
save less because, with the higher interest rate, lower savings could actually generate more
future consumption.
Diff: 1
Topic: Effects of A Price Change

2) Many manufacturers sell products labeled as having imperfections at a discount at their

factory outlets but do not ship these imperfect goods to regular retail outlets. Why?

Answer: There is some substitutability between the goods, but imperfects sell for a lower
price. Suppose, for example, the good sells for $2, but imperfects sell for $1. Both goods cost
the same to ship, say $1. As a result, the relative price of an imperfect at a factory outlet is
(1/2) but rises to (2/3) at the retail outlet, where imperfects will not sell because of the higher
relative price.
Diff: 1
Topic: Effects of a Price Change

3) Why can't all goods be inferior?

Answer: If all goods were inferior, an increase in income would lead to a decline in the
quantity demanded for all goods. This, however, would leave the consumer below the budget
line and therefore not achieving the highest utility possible.
Diff: 1
Topic: How Income Changes Shift Demand Curves

Figure 5.6

4) Figure 5.6 shows three different Engel curves. Rank them in terms of income elasticity.

Answer: Engel curve A implies that a certain level of income is required before any of the
good is purchased. Engel curve B implies that the quantity demanded is proportional to

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income (unit elastic). Engel curve C implies that the good is a necessity since it would be
consumed even if income were zero. Thus A > B > C.
Diff: 2
Topic: How Income Changes Shift Demand Curves

5) When income increases by 1%, the quantity demanded of a good decreases by 2%.
What is the income elasticity of the good? Is the good normal or inferior? Why?

Answer: The income elasticity is -2. The good is inferior because the income elasticity is
negative.
Diff: 1
Topic: How Income Changes Shift Demand Curves

Figure 5.7

6) Draw budget constraints, indifference curves, and the income consumption curve for a
good that has an income elasticity that is perfectly inelastic.

Answer: See Figure 5.7.

Diff:1
Topic: How Income Changes Shift Demand Curves

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Figure 5.8

7) Draw two graphs, one directly above the other. On the upper graph, label the
vertical axis Good X and label the horizontal axis Good Y. On the lower graph, label the
vertical axis the Price of Good Y and label the horizontal axis Good Y. In the upper graph,
show the income and substitution effects of a decrease in the price of good Y when Y is a
Giffen good. Draw the corresponding demand curve for good Y in the lower graph.

Answer: See Figure 5.8. Point A is the original consumption point. The movement from
point A to point B is the substitution effect. The movement from point B to point C is the
income effect.
Diff:2
Topic: Deriving Demand Curves

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Figure 5.9

8) Figure 5.9 shows a consumer's indifference curves for soda and all other goods. Assuming a
budget of $100, derive the consumer's demand for soda for prices of $4 and $10 per case of
soda. Estimate the price elasticity of demand for soda.

Answer: At a price of $4, 15 cases are purchased, At a price of $10, 6 cases are purchased. In
both cases, the same total amount, $60, is spent on soda. This implies unit elasticity.
Diff: 1
Topic: Deriving Demand Curves

9) Use the Slutsky equation to show that a Giffen good must be an inferior good, BUT an
inferior good need not be a Giffen good.

Answer: The Slutsky equation may be written as dQ/dpTotal = dQ/dpsubs - (dQ/dI). For a
Giffen good, dQ/dpTotal is positive, which implies that -(dQ/dI) must be positive and large
enough to offset dQ/dpsubs, which is always negative. For any inferior good, however,
-(dQ/dI) is positive but not necessarily large enough to make dQ/dpTotal positive.
Diff: 1
Topic: Deriving Demand Curves

10) Suppose the typical consumer only purchases food and clothing, and her utility can be
expressed as U = F * C. Currently, food costs $5 per unit and clothing costs $2 per unit. Her
income is $70. If the price of food increases to $6, compare the resulting Laspyre's price
index with a true cost of living index.

Answer: Maximizing utility subject to the initial constraint (5F + 2C = 70) yields C/F = 5/2
or F = 7 and C = 17.5. The Laspyre's price index calculates the ratio of the income necessary
to achieve the original bundle relative to the original income. In this case [(6*7) +
(2*17.5)]/70 = 1.10. The true cost of living index calculates the ratio of the income necessary
to achieve the original level of utility relative to the original income. Utility is held constant

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when C*F = 17.5*7=122.5. The consumer is on the new budget line when C/F =3.
Combining yields F= 6.39 and C = 19.17. At the new prices, this requires an income of 76.68
and a resulting cost of living index of 76.68/70 = 1.095.
Diff: 2
Topic: Cost-of-Living Adjustments

Figure 5.10

11) Figure 5.10 shows an indifference map for a person's choices between leisure and
consumption. Derive this person's labor supply curve for wage rates of $5, $10, and $15.

Answer: This person's labor supply curve is downward sloping. The three coordinates for
w,H are approximately (5,14), (10,11), and (15,9).
Diff: 1
Topic: Deriving Labor Supply Curves

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Figure 5.11

12) Draw a graph with Goods Per Day on the vertical axis and Leisure Hours Per Day
increasing from left to right on the horizontal axis. Show that a person who works can work
fewer hours and increase utility when the wage rate increases.

Answer: See Figure 5.11.

Diff: 1
Topic: Deriving Labor Supply Curves

13) Suppose a person's utility for leisure (L) and consumption (Y) can be expressed as U = Y +
L0.5. Show what happens to the person's labor supply curve when the income tax is cut from
70 percent to 30 percent.

Answer: Since Y = net income, U = w(1-t)H + (24-H)0.5. Maximizing utility with respect to
hours worked, H, yields H = 24 - (2(1-t)w)-2. Any decrease in t would increase the number of
hours worked. Note: this person is a workaholic. Even at a net wage of $1, this person only
relaxes for 3/4 of an hour!
Diff: 1
Topic: Deriving Labor Supply Curves

14) Suppose a person's utility for leisure (L) and consumption (Y) can be expressed as U = Y +
L0.5. Assuming a wage rate of $10 per hour, show what happens to the person's labor supply
curve when the person wins a lottery prize of $100 per day.

Answer: Rearranging yields U = (Y* + 10H) + (24-H)0.5. Maximizing utility with respect to
H yields H = 23.9975 hours. Note: H is not a function of Y* because the marginal utility of
leisure is independent of income. Thus, the person's labor supply curve is not affected by
winning the lottery.
Diff: 2
Topic: Deriving Labor Supply Curves

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15) Suppose a person's utility for leisure (L) and consumption (Y) can be expressed as U = Y * L
and this person has no non-labor income. Assuming a wage rate of $10 per hour, show what
happens to the person's labor supply when the person wins a lottery prize of $100 per day.

Answer: Rearranging yields U = ( Y* + 10H) * (24 - H) = 24 Y* + 240H - Y*H - 10 H2.

Maximizing utility with respect to H yields dU/dH = 240 - Y*- 20H = 0. Before winning the
lottery, Y*= 0, so H = 12. After winning the $100 per day lottery, Y*= 100, so H = 7. Winning
the lottery reduces this person's quantity of labor supplied by 5 hours when w = $10.
Diff: 2
Topic: Deriving Labor Supply Curves

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